| The rolling mill's transmission shaft system, which transmits the rotating mechanical energy to roller, is an important component of the rolling mill. With the improvement of the rolling speed and intensity, the abnormal instability phenomenon offen occurs due to the torsional vibration of the rolling mill's transmission shaft system. The torsional vibration causes fatigue damage and life reduction of the rolling parts. Furthermore, the torsional vibration affects products quality and production efficiency. Suppression torsional vibration of the rolling mill's transmission shaft system is the key to stable operation of rolling mill. However, the accurate model of Torsional vibration is the basis of suppression torsional vibration. Research on the model of torsional vibration is very important for main drive system of rolling mill to reform optimum design, performance analysis, failure monitor and process control.The rolling mill's transmission shaft system model of torsional vibration was proposed, on the basis of torsional vibration mechanism was analysed, the nonlinear dynamics behaviour of rolling mill's torsional oscillation system was studied. Through the theoretical analysis and the numerical calculation, the nonlinear vibration, nonlinear dynamic response, stability, bifurcation and chaotic behavior of rolling mill's torsional system were studied under the influence by nonlinear rigid, nonlinear friction of roller. The multi mechanics and the evolvement ruler of nonlinear vibration on rolling mill's drive system were obtained. The study has some theoretics meaning and engineering application value.Firstly, on the basis of torsional vibration dynamic model, the torsional vibration linear model of the simplified rolling mill's drive system was established, and the model under mutation loading and cyclic loading were studied. A kind stickiness flexibility torsional vibration dynamics equation was established, steadiness of relatively rotation angle was discussed. Gaining solution for a kind stickiness flexibility coefficient because the equation was non-homogeneous ordinary differential equation group of order 2 linear of variable coefficient, and there isn't unified solution to this equation group.Second, based on the torsional vibration dynamic model possessing linear rigidity and nonlinear damping force and forcing periodic force, the stability of autonomous nonlinear dynamical system was discussed, by using Lyapunov stability theory. Asymptotically stable periodic solution on principal resonance of the model was obtained, by applying average method. 3ultraharmonic resonance and 1/3subharmonic resonance solution of the model were obtained, by multiscale method.Thirdly, the acquisition method of precise periodic signal and uniqueness of periodic solutions for the two kind of torsional vibration nonlinear dynamic model were investigated. The necessary condition of uniqueness of periodic solutions of the model was presented by using qualitative analysis method. The acquisition method of precise periodic signal of the model was given under certain condition .Fourthly, the chaotic behavior of rolling mill torsional vibration system was studied, the critical condition of chaotic motion was obtained by Melnikov function method. The necessary condition of chaos of the system was obtained. On the basis of combined excitation of harmonic and random inputs, the resonance of the system to random excitation was investigated, the steady syate solution of system was obtained.Finally, stability solution of rolling mill's transmission shaft torsional vibration system with paramedical-highly excitations was investigated by using asymptotic method and multiscale method. Using qualitative analysis method, chaotically and periodic motion of the system were researched. Bifurcations of harmonic solution and sub-harmonic solution for the system were discussed by the theory of Poincaré. At last, chaotic motion of the system was studied by Melnikov function.
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